Given a Seifert form , choose a basis , ..., for as a -module so every element is uniquely expressible as
(1)
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with integer. Then define the Seifert matrix as the integer matrix with entries
(2)
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For example, the right-hand trefoil knot has Seifert matrix
(3)
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A Seifert matrix is not a knot invariant, but it can be used to distinguish between different Seifert surfaces for a given knot.